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Abstract

The quantum Hall effect is investigated in a high-mobility two-dimensional
electron gas on the surface of a cylinder. The novel topology leads to a
spatially varying filling factor along the current path. The resulting
inhomogeneous current-density distribution gives rise to additional features in
the magneto-transport, such as resistance asymmetry and modified longitudinal
resistances. We experimentally demonstrate that the asymmetry relations
satisfied in the integer filling factor regime are valid also in the transition
regime to non-integer filling factors, thereby suggesting a more general form
of these asymmetry relations. A model is developed based on the screening
theory of the integer quantum Hall effect that allows the self-consistent
calculation of the local electron density and thereby the local current density
including the current along incompressible stripes. The model, which also
includes the so-called `static skin effect' to account for the current density
distribution in the compressible regions, is capable of explaining the main
experimental observations. Due to the existence of an
incompressible-compressible transition in the bulk, the system behaves always
metal-like in contrast to the conventional Landauer-Buettiker description, in
which the bulk remains completely insulating throughout the quantized Hall
plateau regime.

We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments.

The electron and current density distributions in the close proximity of quantum point contacts (QPCs) are investigated. A three dimensional Poisson equation is solved self-consistently to obtain the electron density and potential profile in the absence of an external magnetic field for gate and etching defined devices. We observe the surface charges and their apparent effect on the confinement potential, when considering the (deeply) etched QPCs. In the presence of an external magnetic field, we investigate the formation of the incompressible strips and their influence on the current distribution both in the linear response and out of linear response regime. A spatial asymmetry of the current carrying incompressible strips, induced by the large source drain voltages, is reported for such devices in the non-linear regime.